1. Field of the Invention
The present invention relates to a method of determining multiphase flow parameters of a porous medium such as a rock, from the interpretation of displacement experiments.
2. Description of the Prior Art
Determination of multiphase flow parameters, such as the relative permeabilities and the capillary pressure, is a major challenge within the context of oilfield development, whether in the reservoir evaluation or when starting production. Laboratory experiments carried out under reservoir pressure and temperature conditions are commonly performed to determine these parameters in a representative manner. In particular, the relative permeabilities are conventionally obtained by means of displacement experiments. The relative permeabilities are then obtained via an analytical and numerical experimental data interpretation so as to take account of all the physical phenomena (capillary pressure, gravity) that influence the experimental data obtained.
The following documents, mentioned in the course of the description hereafter, illustrate the state of the art:                Courtial R. and Ghalimi S., “Techniques for Relative Permeability Calculations: A Closer Look”, SCA No.2000-47, Society of Core Analysts, Abu-Dhabi, 2000,        Dauba C., Hamon G., Quintard M. and Cherblanc F., “Identification of Parallel Heterogeneities with Miscible Displacement”, SCA No.9933, Society of Core Analysts, Denver, Colo., 1999,        Fincham A. and Gouth F., “Improvements of Coreflood Design and Interpretation Using a New Software”, SCA No.2000-19, Society of Core Analysts, Abu-Dhabi, 2000,        Goodfield M., Goodyear S. G. and Townsley P. H., “New Coreflood Interpretation Method for Relative Permeabilities Based on Direct Processing of In-Situ Saturation Data”, SPE No.71490, Annual Technical Conference and Exhibition, New Orleans, La., 2001,        Graue A., 1994, “Imaging the Effects of Capillary Heterogeneities on Local Saturation Development in Long Corefloods”, SPE Drilling & Completion, v. March, pp. 57-64,        Honarpour M. M., Cullick A. S. and Saad N., “Influence of Small-Scale Rock Laminations on Core Plug Oil/Water Relative Permeability and Capillary Pressure”, SPE No.27968, Centennial Petroleum Engineering Symposium, Tulsa, OK, 1994,        Mejia G. M., Mohanty K. K. and Watson A. T., 1995, “Use of In-Situ Saturation Data in Estimation of Two-Phase Flow Functions in Porous Media”, Journal of Petroleum Science and Engineering, v. 12, pp. 233-245.        
The commonest approach for determining the multiphase flow parameters of a porous medium such as a rock uses a homogeneous numerical model to describe the rock sample. The mean value of the petrophysical properties (permeability, porosity) of the sample is in this case assigned to any point thereof. A single relative permeabilities/capillary pressure set is also used for the entire sample. Displacement experiments are then interpreted by means of a flow simulator which essentially is an inversion loop. This inversion loop allows adjustment of the values of the multiphase flow parameters by minimizing an objective function expressing the difference between the simulation and the experimental results.
The local saturation data are then used globally with the other experimental data (differential pressure ΔPi (t), displaced fluid production V(t)) to calculate the objective function. At each iteration, this function is minimized by adjusting the relative permeability curves (at the same time as the capillary pressure curves sometimes). Several publications have shown the added value of the local saturation measurements in the inversion process, in particular for low injected fluid saturation values (Courtial and Ghalimi, 2000). However, the numerical saturation profiles (from the flow simulator) can reproduce only globally the measured profiles since the numerical model is based on a homogeneous description. In other words, the local heterogeneity is not taken into account.
Now, it is well-known that this heterogeneity has an impact on local measurements. In fact, whatever the protocol chosen to select rock samples (CT-scanner, mercury-pump porosimetry, tracer test), the petrophyscial properties of these rocks are often heterogeneous at the scale of a core (Dauba et al., 1999). Various authors have furthermore shown the existence of atypical saturation profiles due to the presence of local heterogeneities within the sample used. Graue (1994) has detailed an interesting petrophysical survey carried out on an eolian sandstone initially considered to be homogeneous. It has been possible to interpret the origin of local saturation fluctuations from local permeability and capillary pressure values. Honarpour et al. (1994) have shown by means of several displacement experiments carried out on samples comprising laminations that the structure of the heterogeneity itself plays an important part in the shape of the relative permeability curves obtained by means of the usual interpretation process. These works show that the local heterogeneity of the rock actually affects the experimentally obtained saturation profiles.
Mejia and Mohanty (1995) have then suggested improving the previous procedure by inverting also the local capillary pressure value. Better fitting has thus been obtained but, as a result of the number of parameters to be adjusted within the scope of optimization, this approach is not very fast and in practice it is not applicable for saturation profiles comprising tens of points.
A more recent approach directly uses the saturation data (Goodfield et al., 2001). The specific feature of this approach is that it bypasses the local heterogeneity problem by smoothing the experimental saturation profiles and that it uses the profiles as input data for the numerical simulator. On the other hand, this approach leads to a noise-containing differential pressure in the course of time, which is not physical since it should always be smooth whatever the heterogeneity degree within the sample.
Another approach is detailed by Fincham and Gouth (2000), who present an interesting analysis of a multi-flow rate displacement experiment showing non-homogeneous saturation profiles. Reproduction of the local saturation fluctuations was improved by introducing several capillary pressure curves so as to take account of the local heterogeneity. Existing surveys have shown that this approach allows obtaining considerable interpretation quality gains but, since adjustment occurs manually, it is only applicable for a limited number of relative permeability/capillary pressure models.
Quite recent generalization of the acquisition of local saturation data has allowed considerable improvement of the degree of analysis and interpretation of the experiments carried out in petrophysics laboratories. SCAL (Special Core Analysis Laboratories) type experiments are then commonly mentioned. The saturation measurements are often affected by the local heterogeneities of the rock, thus exhibiting a non-smooth form which is difficult to reproduce by means of numerical simulation. The various methods currently available in the industry are not satisfactory because they do not take account of the existence of the local heterogeneity of the rock in the relative permeabilities inversion from the experimental data. The method hereafter overcomes this drawback with the double objective of improving the interpretation quality while taking account of the influence of the heterogeneity of the rock on the results obtained.